I have heard that the FDG scan will detect neuroendocrine cancer, here is some information about that.

From NIH Frontiersin and LWW

Yes, an FDG scan (FDG-PET/CT) can detect neuroendocrine prostate cancer (NEPC), especially in cases where the disease is aggressive or advanced.
• FDG-PET has demonstrated clinical utility in detecting metastatic disease in patients with NEPC and can also be used to monitor treatment response and tumor viability.
• NEPC and aggressive prostate cancers often show increased glucose metabolism, making them more visible on FDG scans, unlike typical prostate adenocarcinoma where FDG-PET is less sensitive.
• In some cases, NEPC lesions may be FDG-avid even when PSMA-based scans are negative, so FDG-PET can be particularly valuable in these settings.
• However, some low-grade neuroendocrine tumors may not be intensely FDG-avid and could be better visualized with other tracers like 68Ga-DOTATATE